Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
Cones and ping-pong in three dimensions

Gabriel Frieden, Félix Gélinas and Étienne Soucy

Vol. 17 (2024), No. 1, 11–28
Abstract

We study the hypergeometric group in GL 3() with parameters α = (1 4, 1 2, 3 4) and β = (0,0,0). We give a new proof that this group is isomorphic to the free product 4 2 by exhibiting a ping-pong table. Our table is determined by a simplicial cone in 3, and we prove that this is the unique simplicial cone (up to sign) for which our construction produces a valid ping-pong table.

Keywords
hypergeometric group, free product of groups, ping-pong lemma
Mathematical Subject Classification
Primary: 20E06
Milestones
Received: 25 January 2022
Revised: 22 November 2022
Accepted: 17 December 2022
Published: 15 March 2024

Communicated by Jim Haglund
Authors
Gabriel Frieden
Université du Québec à Montréal
Montréal, QC
Canada
Félix Gélinas
Université du Québec à Montréal
Montréal, QC
Canada
Étienne Soucy
Université du Québec à Montréal
Montréal, QC
Canada